The following is

To find: The median height.

Formula Used:

Median = l + × h

l = lower limit of median class

f = frequency of median class

h = size of the median class

F = cumulative frequency preceding the median class.

Explanation:

We have, N = 420

= 210

The cumulative frequency just greater than is 275 then 165.5-168.5 is the median class such that,

l = 165.5, f = 142, F = 133 and h = 168.5-165.5 = 3

Median = l + × h

= 165.5 + × 3

= 165.5 + × 3

= 165.5 + 1.63

= 167.13